cp's OEIS Frontend

A347054 Number of domino tilings of a 32 X n rectangle.

%I A347054 #17 Sep 14 2021 04:44:54
%S A347054 1,1,3524578,1117014753,170220478472105,224916047725262248,
%T A347054 12348080425980866090537,30648981125778378496845537,
%U A347054 1010618564986361239515088848178,3596059736380751648485086101179655,87171995375835553001398855677616476448,391978133958466896956216157693001644153072
%N A347054 Number of domino tilings of a 32 X n rectangle.
%C A347054 It is known that the number of domino tilings of an m X n rectangle is equal to the number of perfect matchings in the m X n grid graph.
%D A347054 A. M. Magomedov, T. A. Magomedov, S. A. Lawrencenko, Mutually-recursive formulas for enumerating partitions of the rectangle, [in Russian, English summary], Prikl. Diskretn. Mat., 46 (2019), 108-121. DOI: 10.17223/20710410/46/9
%D A347054 A. M. Magomedov and S. A. Lavrenchenko, Computational aspects of the partition enumeration problem, [in Russian, English summary], Dagestan Electronic Mathematical Reports, 14 (2020), 1-21. DOI: 10.31029/demr.14.1
%H A347054 M. E. Fisher, <a href="https://doi.org/10.1103/PhysRev.124.1664">Statistical mechanics of dimers on a plane lattice</a>, Phys. Rev., 124 (1961), 1664-1672.
%H A347054 P. W. Kasteleyn, <a href="https://doi.org/10.1016/0031-8914(61)90063-5">The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice</a>, Physica, 27 (1961), 1209-1225.
%H A347054 P. W. Kasteleyn, <a href="https://doi.org/10.1063/1.1703953">Dimer statistics and phase transitions</a>, J. Math. Phys., 4 (1963), 287-293.
%H A347054 V.-H. Nguyen, K. Perrot, M. Vallet, <a href="https://doi.org/10.1016/j.tcs.2020.04.007">NP-completeness of the game Kingdomino{TM}</a>, Theoret. Comput. Sci., 822 (2020), 23-35.
%F A347054 a(n) = Product_{j=1..16} (Product_{k=1..floor(n/2)}(4*(cos(j*Pi/33))^2+ 4*(cos(k*Pi/(n+1)))^2)) (special case of the double product formula in A099390).
%t A347054 Do[ P=1;
%t A347054 Do[P=P*4*(Cos[Pi*i/(n+1)]^2+Cos[Pi*j/33]^2), {i,1,n/2}, {j,1,16}];
%t A347054 Print["n=", n ,":", Round[P]], {n,1,11000}]
%Y A347054 Cf. A099390, A340532.
%Y A347054 Column n=32 of A187596.
%K A347054 nonn
%O A347054 0,3
%A A347054 A. M. Magomedov and _Serge Lawrencenko_, Aug 14 2021